Oort's conjecture on direct sums of Newton polygons of curves
For , let be positive integers, let be symmetric Newton polygons of height , and let . Define to be the symmetric Newton polygon of height obtained by taking the union of the slopes of and , with the multiplicity of each slope equal to the sum of its multiplicities in and .
Oort's conjecture. If occurs on for , then occurs on .
This conjecture predicts that Newton polygons realized by curves can be combined through direct sum. The paper studies some cases of the conjecture, while the general assertion remains open.
References
Primary source
Rachel Pries, “Some cases of Oort's conjecture about Newton polygons”, arXiv:2306.11080 (2024).
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